Crystals of type 𝐷_{𝑛}⁽¹⁾ and Young walls

Lee, Hyeonmi

doi:10.1090/S0002-9947-05-03846-8

Crystals of type $D_n^{(1)}$ and Young walls
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Trans. Amer. Math. Soc. 358 (2006), 1847-1867 Request permission

Abstract:

We give a new realization of arbitrary level perfect crystals and arbitrary level irreducible highest weight crystals of type $D_n^{(1)}$, in the language of Young walls. We refine the notions of splitting of blocks and slices that have appeared in our previous works, and these play crucial roles in the construction of crystals. The perfect crystals are realized as the set of equivalence classes of slices, and the irreducible highest weight crystals are realized as the affine crystals consisting of reduced proper Young walls which, in turn, are concatenations of slices.

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